In Batman Begins, Ra's al Ghul is Bruce's mentor and Batman leaves him to die, we're not sure if he dies. And if he dies he could be brought back with the Lazarus Pit.
In the Arrowverse, Merlyn also has Ra's al Ghul as his mentor. Ra's wants Oliver to take over his role as Head of the Demon, Oliver kills Ra's and hereby becomes the new Ra's al Ghul. He then gives the position to Malcolm Merlyn.
What is the synchronicity between these character? Are they in the same timeline, the same person or do they lives in another universe (in the multiverse that we get to know in the Flash)?
I haven't read any of the comics, I saw the Christopher Nolan Batman movies, the Arrow, the Flash and Supergirl.
I read the following links but they didn't made it clear to me: